1202.3969 (F. Falceto et al.)

Reduction of Lie-Jordan Banach algebras and quantum states    [PDF]

F. Falceto, L. Ferro, A. Ibort, G. Marmo

A theory of reduction of Lie-Jordan Banach algebras with respect to either a
Jordan ideal or a Lie-Jordan subalgebra is presented. This theory is compared
with the standard reduction of C*-algebras of observables of a quantum system
in the presence of quantum constraints. It is shown that the later corresponds
to the particular instance of the reduction of Lie-Jordan Banach algebras with
respect to a Lie-Jordan subalgebra as described in this paper. The space of
states of the reduced Lie-Jordan Banach algebras is described in terms of
equivalence classes of extensions to the full algebra and their GNS
representations are characterized in the same way. A few simple examples are
discussed that illustrates some of the main results.

View original: http://arxiv.org/abs/1202.3969